| Abstract: | The H∞-control problem with a non-zero initial condition for infinite dimensional systems is considered The initial conditions are assumed to be in some subspace. First the H∞ problem with full information is considered and necessary and sufficient conditions for the norm of an input-output operator to be less than a given number are obtained, The characterization of all admissible controllers is also given. This result is then used to solve the general H∞ control problem and the filtering problem with initial uncertainty. The filtering problem on finite horizon involves the estimate of the state at final time. The set of all suboptimal filters is given both on finite and infinite horizons. |
